Suite can apply to hotel rooms, office space, or even software. But whence cometh it and why? And does "sweet" merely exist as a coincidence or did it diverge from a common root somewhere in the era when Shakespeare was spelling his name in multiple ways?

Both suite and suit come via French from the Latin verb sequi, to follow. I suppose the idea is of a set of things "following on" from one another. Sect, and in some senses set, come from the same root. Sweet is entirely unrelated.

Another meaning of suite is a set of musical pieces. Hence Tchaikovsky's Nutcracker Suite, which is a set of orchestral pieces selected from the music of his Nutcracker ballet. This is sometimes misinterpreted as "Nutcracker Sweet", especially as sweets feature in the story.